I agree. We should be teaching this (and Dirac's "derivation" of the Dirac equation) in undergrad physics to motivate what creative thinking in physics looks like.
Yes you can, and the derivation is essentially done in many textbooks. Heisenberg, however, did it wrong in his first paper. Because these matrices are finite dimensional for a specific angular momentum representation, they are easier to work with.
It didn't in the Bohr-Sommerfeld theory. It is what classical mechanics predicts. If an orbit is periodic, then the theory of Fourier series says a function that is periodic in time can be expanded in terms of oscillating functions using the fundamental frequency and its harmonics only. But, this is not what was observed in spectra.
@@quantum4everyone I'm confused, why is the spectrum of hydrogen tied to the fourier expansion of the classical position function of a single electron?
@@whatno5090 In the olden days, quantum mechanics was viewed as a restriction on classical mechanics. So, the start of evaluating something quantum mechanically is to do so classically and then apply a restriction. The classical analysis always involves harmonics, so this is what you would expect to see in the spectra of something with periodic orbits. Experiment showed this to be incorrect, which is when the Bohr-Sommerfeld quantization condition was developed, but that was also erroneous. Then Heisenberg figured out how to properly incorporate the correct spectra into the theory with his matrix mechanics.
@@quantum4everyone My confusion here doesn't lie in the jump from classical to quantum, it lies entirely in the classical. Let's pretend quantum mechanics as a field didn't even exist. Purely classically, why would we expect the fourier expansion of the classical position function of a single electron, to be related to the hydrogen spectrum? I'm asking this because I don't know the relative classical mechanics which would lead to such a belief.
@@whatno5090in classical mechanics everything is determined by the function of position versus time. If periodic this is given by a Fourier series. So if you want to build quantum from classical, which was the strategy, that is what you do.
QM classicalized in 2010. Forgotten Physics website uncovers the hidden variables and constants and the bad math of Wien, Schrodinger, Heisenberg, Einstein, Debroglie,Planck, Bohr etc.
@@sebastiangudino9377 Further “The Final Theory: Rethinking Our Scientific Legacy “, Mark McCutcheon for proper physics including the CAUSE of gravity, electricity, magnetism, light and well.... everything. Yes all Standard Theory/Model was provided/ maintained by “crockpots.” So goes progress.
incredibily good and short review of the basics and origin of matrix mechanics. Precious stuff. Thanks a lot
You are very welcome.
I agree. We should be teaching this (and Dirac's "derivation" of the Dirac equation) in undergrad physics to motivate what creative thinking in physics looks like.
Thanks you for sharing! Looking forward for more content, great quality!
You are very welcome
Succinct and wondrous. Beautiful. thx for posting.
Glad you liked it
Could you use the matrix mechanics to solve the rigid rotor? Thanks professor
Yes you can, and the derivation is essentially done in many textbooks. Heisenberg, however, did it wrong in his first paper. Because these matrices are finite dimensional for a specific angular momentum representation, they are easier to work with.
Beautiful…
Could somebody explain why old quantum theory predicted harmonics in the atomic spectra?
It didn't in the Bohr-Sommerfeld theory. It is what classical mechanics predicts. If an orbit is periodic, then the theory of Fourier series says a function that is periodic in time can be expanded in terms of oscillating functions using the fundamental frequency and its harmonics only. But, this is not what was observed in spectra.
@@quantum4everyone I'm confused, why is the spectrum of hydrogen tied to the fourier expansion of the classical position function of a single electron?
@@whatno5090 In the olden days, quantum mechanics was viewed as a restriction on classical mechanics. So, the start of evaluating something quantum mechanically is to do so classically and then apply a restriction. The classical analysis always involves harmonics, so this is what you would expect to see in the spectra of something with periodic orbits. Experiment showed this to be incorrect, which is when the Bohr-Sommerfeld quantization condition was developed, but that was also erroneous. Then Heisenberg figured out how to properly incorporate the correct spectra into the theory with his matrix mechanics.
@@quantum4everyone My confusion here doesn't lie in the jump from classical to quantum, it lies entirely in the classical.
Let's pretend quantum mechanics as a field didn't even exist. Purely classically, why would we expect the fourier expansion of the classical position function of a single electron, to be related to the hydrogen spectrum?
I'm asking this because I don't know the relative classical mechanics which would lead to such a belief.
@@whatno5090in classical mechanics everything is determined by the function of position versus time. If periodic this is given by a Fourier series. So if you want to build quantum from classical, which was the strategy, that is what you do.
QM classicalized in 2010. Forgotten Physics website uncovers the hidden variables and constants and the bad math of Wien, Schrodinger, Heisenberg, Einstein, Debroglie,Planck, Bohr etc.
Crackpot?
@@sebastiangudino9377 Further “The Final Theory: Rethinking Our Scientific Legacy “, Mark McCutcheon for proper physics including the CAUSE of gravity, electricity, magnetism, light and well.... everything. Yes all Standard Theory/Model was provided/ maintained by “crockpots.” So goes progress.